Current visualizations in microbiome research rely on aggregations in taxonomic classifications or do not show less abundant taxa. We introduce Snowflake: a new visualization method that creates a clear overview of the microbiome composition in collected samples without losing any information due to classification or neglecting less abundant reads. Snowflake displays every observed OTU/ASV in the microbiome abundance table and provides a solution to include the data's hierarchical structure and additional information obtained from downstream analysis (e.g., alpha- and beta-diversity) and metadata. Based on the value-driven ICE-T evaluation methodology, Snowflake was positively received. Experts in microbiome research found the visualizations to be user-friendly and detailed and liked the possibility of including and relating additional information to the microbiome's composition. Exploring the topological structure of the microbiome abundance table allows them to quickly identify which taxa are unique to specific samples and which are shared among multiple samples (i.e., separating sample-specific taxa from the core microbiome), and see the compositional differences between samples. An R package for constructing and visualizing Snowflake microbiome composition graphs is available at https://gitlab.com/vda-lab/snowflake.